{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "(到目前为止，您一直使用渐变下降来更新参数并将成本降至最低。在这款笔记本中，您将学习更先进的优化方法，可以加快学习速度，甚至可以让您获得更好的成本函数最终价值。有一个好的优化算法可以是等待几天之间的差异，只是几个小时才能得到一个好的结果)\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\ChengzhiYang\\深度学习作业\\第二课第二周编程作业\\assignment2\\opt_utils.py:76: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], layer_dims[l-1])\n",
      "C:\\Users\\ChengzhiYang\\深度学习作业\\第二课第二周编程作业\\assignment2\\opt_utils.py:77: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], 1)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "(机器学习中一个简单的优化方法是梯度下降（GD）。当您对每个步骤的所有m个样本采取这个步骤时，它也被称为批处理梯度下降（Batch Gradient Descent）)\n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate*grads[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] -learning_rate*grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost = compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost = compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "（在随机梯度下降中，在更新梯度之前，只使用1个训练样例。当训练集大时，SGD可以更快。但是这些参数会向最小值“摆动”而不是平稳地收敛。这是一个例子演示）\n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m)) #随机排列\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, k * mini_batch_size : (k+1) * mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:, k * mini_batch_size : (k+1) * mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "\n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:, num_complete_minibatches * mini_batch_size : m]\n",
    "        mini_batch_Y = shuffled_Y[:, num_complete_minibatches * mini_batch_size : m]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "\n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 20)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 20)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l + 1)] = beta*v[\"dW\" + str(l + 1)]+(1-beta)*grads['dW' + str(l+1)]\n",
    "        v[\"db\" + str(l + 1)] = beta*v[\"db\" + str(l + 1)]+(1-beta)*grads['db' + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l + 1)] = parameters['W' + str(l+1)] - learning_rate*v[\"dW\" + str(l + 1)] \n",
    "        parameters[\"b\" + str(l + 1)] = parameters['b' + str(l+1)] - learning_rate*v[\"db\" + str(l + 1)] \n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "\n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l + 1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        v[\"db\" + str(l + 1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l + 1)] = np.zeros(parameters[\"W\" + str(l+1)].shape)\n",
    "        s[\"db\" + str(l + 1)] = np.zeros(parameters[\"b\" + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "v[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "v[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n",
      "s[\"dW1\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db1\"] = [[0.]\n",
      " [0.]]\n",
      "s[\"dW2\"] = [[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n",
      "s[\"db2\"] = [[0.]\n",
      " [0.]\n",
      " [0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l + 1)] = beta1*v[\"dW\" + str(l + 1)] +(1-beta1)*grads['dW' + str(l+1)]\n",
    "        v[\"db\" + str(l + 1)] = beta1*v[\"db\" + str(l + 1)] +(1-beta1)*grads['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l + 1)] = v[\"dW\" + str(l + 1)]/(1-(beta1)**t)\n",
    "        v_corrected[\"db\" + str(l + 1)] = v[\"db\" + str(l + 1)]/(1-(beta1)**t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l + 1)] =beta2*s[\"dW\" + str(l + 1)] + (1-beta2)*(grads['dW' + str(l+1)]**2)\n",
    "        s[\"db\" + str(l + 1)] = beta2*s[\"db\" + str(l + 1)] + (1-beta2)*(grads['db' + str(l+1)]**2)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l + 1)] =s[\"dW\" + str(l + 1)]/(1-(beta2)**t)\n",
    "        s_corrected[\"db\" + str(l + 1)] = s[\"db\" + str(l + 1)]/(1-(beta2)**t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l + 1)] = parameters[\"W\" + str(l + 1)]-learning_rate*(v_corrected[\"dW\" + str(l + 1)]/np.sqrt( s_corrected[\"dW\" + str(l + 1)]+epsilon))\n",
    "        parameters[\"b\" + str(l + 1)] = parameters[\"b\" + str(l + 1)]-learning_rate*(v_corrected[\"db\" + str(l + 1)]/np.sqrt( s_corrected[\"db\" + str(l + 1)]+epsilon))\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63178673 -0.61919778 -0.53561312]\n",
      " [-1.08040999  0.85796626 -2.29409733]]\n",
      "b1 = [[ 1.75225313]\n",
      " [-0.75376553]]\n",
      "W2 = [[ 0.32648046 -0.25681174  1.46954931]\n",
      " [-2.05269934 -0.31497584 -0.37661299]\n",
      " [ 1.14121081 -1.09245036 -0.16498684]]\n",
      "b2 = [[-0.88529978]\n",
      " [ 0.03477238]\n",
      " [ 0.57537385]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[0.02344157]\n",
      " [0.16598022]\n",
      " [0.07420442]]\n",
      "s[\"dW1\"] = [[0.00121136 0.00131039 0.00081287]\n",
      " [0.0002525  0.00081154 0.00046748]]\n",
      "s[\"db1\"] = [[1.51020075e-05]\n",
      " [8.75664434e-04]]\n",
      "s[\"dW2\"] = [[7.17640232e-05 2.81276921e-04 4.78394595e-04]\n",
      " [1.57413361e-04 4.72206320e-04 7.14372576e-04]\n",
      " [4.50571368e-04 1.60392066e-07 1.24838242e-03]]\n",
      "s[\"db2\"] = [[5.49507194e-05]\n",
      " [2.75494327e-03]\n",
      " [5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    # 每次迭代，都重新随机排列训练集，并按mini_batch_size划分子集，然后对每个子集进行训练（前向、反向传播、成本计算、参数更新）\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690736\n",
      "Cost after epoch 1000: 0.685273\n",
      "Cost after epoch 2000: 0.647072\n",
      "Cost after epoch 3000: 0.619525\n",
      "Cost after epoch 4000: 0.576584\n",
      "Cost after epoch 5000: 0.607243\n",
      "Cost after epoch 6000: 0.529403\n",
      "Cost after epoch 7000: 0.460768\n",
      "Cost after epoch 8000: 0.465586\n",
      "Cost after epoch 9000: 0.464518\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7966666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690741\n",
      "Cost after epoch 1000: 0.685341\n",
      "Cost after epoch 2000: 0.647145\n",
      "Cost after epoch 3000: 0.619594\n",
      "Cost after epoch 4000: 0.576665\n",
      "Cost after epoch 5000: 0.607324\n",
      "Cost after epoch 6000: 0.529476\n",
      "Cost after epoch 7000: 0.460936\n",
      "Cost after epoch 8000: 0.465780\n",
      "Cost after epoch 9000: 0.464740\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.7966666666666666\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.690552\n",
      "Cost after epoch 1000: 0.185501\n",
      "Cost after epoch 2000: 0.150830\n",
      "Cost after epoch 3000: 0.074454\n",
      "Cost after epoch 4000: 0.125959\n",
      "Cost after epoch 5000: 0.104344\n",
      "Cost after epoch 6000: 0.100676\n",
      "Cost after epoch 7000: 0.031652\n",
      "Cost after epoch 8000: 0.111973\n",
      "Cost after epoch 9000: 0.197940\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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